A059172 Numbers k such that k/rad(k) > sqrt(k) where rad(k) is the largest squarefree number dividing k.

8, 16, 27, 32, 48, 54, 64, 72, 81, 96, 108, 125, 128, 144, 160, 162, 192, 200, 216, 224, 243, 250, 256, 288, 320, 324, 343, 375, 384, 392, 400, 405, 432, 448, 486, 500, 512, 567, 576, 625, 640, 648, 675, 686, 704, 729, 768, 784, 800, 832, 864, 896, 960, 968

Offset

1,1

Comments

Numbers k which have measure of smoothness J bigger as 2. Where J = log(k)/log(rad(k)), where rad(k) is product of distinct prime divisors of k. - Artur Jasinski, Feb 02 2010

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

48 is included because 6 is largest squarefree to divide 48 and 48 /6 = 8 > sqrt(48).

Mathematica

aa = {}; Do[kk = FactorInteger[c]; nn = 1; Do[nn = nn*kk[[n]][[1]], {n, 1, Length[kk]}]; If[Log[c]/Log[nn] >= 2, AppendTo[aa, c]], {c, 2, 1000}]; aa (* Artur Jasinski, Feb 02 2010 *)
Select[Range[1000], #/Last[Select[Divisors[#], SquareFreeQ]]>Sqrt[#]&] (* Harvey P. Dale, Dec 14 2017 *)

Crossrefs

Cf. A003557, A007947.

Sequence in context: A083419 A329134 A090081 * A360558 A107606 A354561

Adjacent sequences: A059169 A059170 A059171 * A059173 A059174 A059175

Keyword

nonn

Author

Leroy Quet, Feb 14 2001

Status

approved